The Cox regression model has been used extensively for analyzing censored failure time data often encountered in biomedical studies. Despite the enormous progress in the Cox regression methodology in the last two decades, several important issues remain unresolved. In this project, we propose to derive simultaneous confidence bands for the subject-specific survival curve, to develop valid and efficient methods for handling missing covariate values and to establish the weak convergence of the sequential partial-likelihood score statistics for testing treatment differences with covariate adjustments. These topics are of direct relevance to health research. First, estimating the survival experience of a patient with a given set of covariate values is important in understanding the disease process and in counseling patients. Secondly, covariate measurements are often incomplete in biomedical studies, but the existing methods are invalid or/and inefficient. Thirdly, it is desirable to adjust for other covariates when testing for treatment differences in order to improve the efficiency of the sequential design and/or to correct for baseline imbalance on important prognostic factors. The accelerated failure time (AFT) model, which relates the logarithm of the failure time linearly to the covariates, is quite appealing to medical investigators due to its straightforward interpretation. Furthermore, the rank regression approach to the AFT model tends to be more efficient and more robust than the partial likelihood inference under the Cox model. The lack of fast computing algorithms and its inability to incorporate time-dependent covariates, however, have hindered the practical use of this model. In this project, we intend to develop rank regression methods for the AFT model with time-dependent covariates and to provide useful solutions to the numerical problems. We will also pursue robust and efficient methods for analyzing correlated survival data commonly found in genetic epidemiologic studies and group randomized trials. The asymptotic properties of the new procedures will be rigorously studied with the use of the martingale theory, the theory of empirical processes and other statistical devices. Their numerical characteristics will be investigated through extensive Monte Carlo studies. Illustrations with real data sets will be provided. Finally, user-friendly software will be made available to the public.